Easier than you think

Algebra Level 3

let f f be a function satisfying f ( x y ) = f ( x ) y f(xy) =\frac {f(x)}{y} for all real numbers x x and y y . If f ( 234 ) = 6 f(234) = 6 , what is the value of f ( 18 ) f(18) ?


The answer is 78.

Ahmad Khamis by Ahmad Khamis , 24, Saudi Arabia

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1 solution

Mark Mottian
Aug 5, 2015

f ( 234 ) = f ( 18 ⋅ 13 ) = f ( 18 ) 13 f(234) = f(18 \cdot 13) = \frac {f(18)}{13}

6 = f ( 18 ) 13 6 = \frac {f(18)}{13}

f ( 18 ) = 6 ⋅ 13 = 78 f(18) = 6 \cdot 13 = \boxed{78}

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